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Abstract

Imaging ultracold atomic gases close to surfaces is an important tool for the detailed analysis of experiments carried out using atom chips. We describe the critical factors that need be considered, especially when the imaging beam is purposely reflected from the surface. In particular we present methods to measure the atom-surface distance, which is a prerequisite for magnetic field imaging and studies of atom surface-interactions.

Figures (8)

Fig. 1 Sketch of Imaging Configurations (not to scale). (a) Grazing Incidence Imaging. The imaging beam is reflected off the atom chip surface and the atom cloud (blue circle) produces two shadows. For the direct image, the imaging beam first reflects off the atom chip surface, then interacts with the atom cloud. For the mirror image, the imaging beam first interacts with the atom cloud, then reflects off the atom chip. (b) Normal Incidence Imaging provides the location of the atom cloud relative to the structures on the atom chip surface. (c) Time-of-flight Imaging, where the atom cloud is far from the atom chip surface.

Fig. 2 (a, b) Images without atoms (Iin) with (a) the imaging beam propagating parallel to chip surface and (b) the imaging beam reflected from chip surface with θ = 2°. The dark region at the top is the shadow cast by the chip and its mounting. The red boxes represent the region where the atom cloud would be located in situ or for short times of flight. The strong horizontal fringes are due to diffraction from the edges of the chip. The inclination of the beam allows the diffraction effects to be moved in the image relative to the position of the atom cloud. The circular fringes and other structures are due to small dust particles in the beam path. (c, d) Reflecting the imaging beam off the atom chip surface results in a standing wave (d) and 2 clouds in the image (c) because the atom cloud (blue circle) is passed by two different beam paths. Path (1) is mapped by the imaging system to a real image, path (2) to a mirror image. The image in (c) would lie in the area denoted in (b).

Fig. 3 The total scattered power Psc for trapped condensates at different heights above a wire. The blue and green curves show the result for in-plane and out-of-plane linear polarization of the imaging beam, which have a small relative phase shift caused by the different boundary conditions of the standing wave at the mirror surface. The angle of incidence of the imaging beam θ was 4.2°. The jump in signal between h = 20 and h = 25 is due to wires of different heights obscuring part of the beams (see Fig. 4). Imaging System 2 in section 9 was used in this case.

Fig. 4 (a–c). Imaging close to wires of different heights. The three scenarios show the atom cloud (blue circle) above different parts of the chip in the situation where the atom chip surface has wires of different heights. Shadows cast by the wires into the imaging beam result in part of the cloud not being imaged in each case. (d) Angular aliasing. If a plane wave component scattered by the atom cloud is reflected by the surface (dashed line), it exits under an angle that is already occupied by a wave component that travels directly away from the surface.

Fig. 5 (a) Simulation and (b) experimental data of absorption images for varying distance between the atom cloud and the chip surface. Shown are vertical line densities for different trap distances, with two separate absorption positions emerging as the distance between the atom cloud and the chip increases (Fig. 2). It can be seen that many of the features resulting from interference effects due to the reflecting surface, such as dark fringes where the atoms are located, are well reproduced by the simulation. The good agreement between theory and experiment allows for an accurate calibration of the trap distance from the surface, which in turn allows for precise calibration of the magnetic fields applied to form the magnetic trap. Imaging System 1 in section 9 was used in this case.

Fig. 6 Extracting the height above the chip by Fourier method. (a) Fourier transform Ĩsc(kx) of (b) the scattered intensity Isc(x). The transverse wave vector kx has been translated to the propagation angle β of the corresponding plane wave component. The green curve shows a fit of the model eq. 7 to the data, the red curve shows the envelope
exp(−kx2w2/2), where w is from a fit to the experimental data Isc(x) shown in (b), which shows the scattered intensity profile Isc(x) together with the profile obtained from the fit in Fourier space (green line). (c) Comparing height estimation methods: Taking the distance directly from Isc(x) to obtain h (open circles) and the corresponding result of the Fourier method (filled circles). The experimental control parameter is nearly linear in height above the surface and is related to the magnetic field controlling the magnetic trap. The Fourier approach presents the more stable and less noisy method. (d) Residuals from the direct fitting method of (b), giving a standard deviation of 0.95μm. (e) Residuals from the Fourier fitting method of (a), giving a standard deviation of 0.21μm. Imaging System 2 in section 9 was used in this case.

Fig. 7(left) Orthogonal-angle-of-incidence imaging of an atomic cloud above a broad 100 μm wide Z-shaped trapping wire. (a) The direct image reveals the features on the chip. The atom cloud is just visible in the center of the central broad wire. (b) Processed absorption picture (divided by a reference image without atoms). The atoms are clearly visible and the speckle patterns are reduced. (Imaging System 3 section 9). (right): Longitudinal imaging. (c) in situ image, 80 μm away from the chip surface showing a BEC that has been split by ∼ 45 μm using a RF dressed-state double-well potential. (d) Image of time-of-flight matter-wave interference of two BECs after 15 ms time of flight [27]. (Imaging System 4 section 9).

Fig. 8 (a) Absorption image of a fragmented BEC taken after 5 ms of time-of-flight expansion. The BEC has been formed at a distance of 10 μm from the wire surface. (b) Longitudinal one-dimensional density profile (blue) derived from the absorption image. The noise-level is shown in red. (c) To accentuate the noise-floor of ∼ 2 atoms/μm rms, the same data has been plotted logarithmically. Imaging System 1 in section 9 was used for this image.